First Minister Arlene Foster last night said there were no "insuperable obstacles" to the DUP reaching an agreement with Sinn Fein over an independent investigation into the 'cash for ash' scandal.

Despite days of intensely bitter exchanges between the two parties, they appear to be moving closer to reaching a deal which would ensure the survival of the Executive.

Mrs Foster said that the only remaining bone of contention between the two parties was Sinn Fein's demand that she step aside for four weeks until an investigatory panel published its preliminary report.

However, Stormont sources believe that a solution can be reached which allows that issue to be fudged.

Sinn Fein yesterday published its proposed terms of reference for an independent investigation into the Renewable Heating Incentive (RHI) scandal which is set to cost the taxpayer £490m.

Mrs Foster said: "With the exception of the issue of stepping aside, we believe that the proposals provided to us by Sinn Fein provide a basis for taking an investigation forward.

"Officials have raised a number of technical issues in relation to the proposals, however there do not appear to us to be any insuperable obstacles to agreement being reached.

"Other parties have suggested that rather than the Attorney General appointing a judicial figure, that this appointment function be undertaken by the Lord Chief Justice. We would be equally comfortable with this."

Earlier, the DUP leader had appeared to reject Sinn Fein's plan. Speaking as she left St Comgall's school in Lisnaskea, where she had been fulfilling a long standing engagement, Mrs Foster was asked if she accepted the party's proposals. "No," she replied.

However, her response changed last night.

Both the Alliance party and the TUV have dismissed Sinn Fein's proposed terms of reference for an investigation as grossly inadequate and repeated that only a full public inquiry can establish the truth on RHI.

Mrs Foster said that while she wasn't denying her accountability, her opponents wanted to "be judge, jury and executioner" in the 'cash for ash' scandal.

"It is clear there are many in the political class who do not believe in due process or natural justice.

"They just want me to go, regardless of the fact that there is not a scintilla of evidence of wrongdoing against me," she said.

"I don't roll over to my political opponents. I believe in getting to the truth. I believe in due process for everyone and that everyone is equal before the law and equally subject to the law.

"That has always been the cornerstone of who I am and will be so despite the hysteria."

Restating her determination not to step aside even temporarily, she said: "I remain focused on the stability of Northern Ireland.

"I am focused on finding solutions. I am focused on building the future of this country."

While the DUP broadly accepted Sinn Fein's proposed terms for an RHI investigation, the Alliance party rejected them as a "political fudge which wont inspire public confidence".

Party leader Naomi Long said: "The question must be asked as to why Sinn Fein and the DUP are unwilling to call for a full public inquiry under the Inquiries Act.

"If they have nothing to hide, they have nothing to fear. Any attempt to cobble together a bespoke investigation will raise public concerns there will also be a bespoke outcome."

Under Sinn Fein's proposals, the Attorney General would appoint a judge to head up a panel to investigate the scandal, and emergency legislation would grant powers to compel witnesses and documentation.

"There are a number of flaws with Sinn Fein's ideas - these proposals would require emergency legislation, which will add another 10 days to the process," Mrs Long said.

"In addition, the Attorney General doesn't have the power to appoint a judge to head up any investigation and is appointed by the First Minister and Deputy First Minister, so is not sufficiently independent. There is also no indication witnesses will be under oath."

Mrs Long insisted that a public inquiry remained the way forward.

"The only reason an investigation would be quicker is if it was less thorough," she added.

TUV leader, Jim Allister, said that Sinn Fein's proposals revealed "muddled thinking". He said the Inquiries Act was "already on the shelf with all the powers needed".

And he claimed that the party's proposed terms of reference failed to focus on the vital issue of "the process and facts of how the RHI scheme came to be approved".

Mrs Foster yesterday hit back at her critics by posting a picture on Facebook of a guinea pig wearing pink, heart-shaped glasses below the phrase: "Can't see all the haters when I've got my love glasses on."

Party colleagues, including MLAs Emma Little Pengelly, Pam Cameron, and Christopher Stalford rushed to support the First Minister, while DUP members told her to "stay strong". However, her political opponents were scathing.

Naomi Long questioned the wisdom of Mrs Foster's response: "We're in the teeth of a political and financial crisis, much of it of her making, and the First Minister opts for this. Let's hope love glasses also work for people lying on trolleys, waiting on cancer drugs, suffering benefit cuts, and struggling to pay heating and food bills," she said.